Question

The domain of the function y=x^3-12x+11 is restricted to -3≤x≤3. What is the maximum value of the function?

Answer 1

first identify the local max then compare that to f(3) , one of those will be absolute max for restricted domain

Answer 2

local max --> set derivative = 0

3x^2 -12 = 0
x = +-2

its a positive cubic function so slope is increasing....local max comes first then local min
f(-2) = 27

f(3) = 2

thus 27 is max for given domain

Answer 3

you can also check with graphing

http://www.wolframalpha.com/input/?i=plot+x%5E3+-12x%2B11+for+x%3D-3+to+3